If the plan is approved by the town council later this month, smokers who light up in public could face on-the-spot fines of up to £100.
Despite having received four petitions from local people and businesses against the ban, town councillor Paul Bartlett said he was confident it would get the go-ahead.
Newsagent Malin Jobanputra said it would have a devastating impact on the local pub trade, but believed his business would be left unscathed. "People will still smoke, they'll just do at home," he added.
Earlier this year smoking was banned in most outdoor public areas in New York, including parks and Times Square.
Meanwhile, the Welsh government has announced that it could soon become the first European country to ban smoking in all vehicles carrying children.
In a public address First Minister Carwyn Jones said it would be the "next logical step" following the ban on smoking in enclosed environments such as offices, pubs and restaurants.
"Children are particularly at risk from second-hand smoke, especially in vehicles where a confined space means there is no respite from the harm of toxic chemicals," she said.
"We will not shy away from considering the introduction of progressive legislation to further protect children from second-hand smoke."